document.write( "Question 1121103: Susie buys 2 pieces of salmon, each weighing x pounds, and 1 piece of trout,y pounds, where x and y are integers. The salmon costs $3.50 per pound and the trout costs $5 per pound. If the total cost of the fish was $77, what could be the value of y? \n" ); document.write( "

Algebra.Com's Answer #736864 by solver91311(24713) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( "2 times 3.50 times

is the amount spent on salmon. 5 times

is the amount spent on trout and the total amount spent is 77.\r
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\n" ); document.write( "\n" ); document.write( "

\r
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\n" ); document.write( "\n" ); document.write( "Which will be more convenient to represent as:\r
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\n" ); document.write( "\n" ); document.write( "

\r
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\n" ); document.write( "\n" ); document.write( "Since the weights in this problem must be positive integers, the smallest possible value for either

would be 1.\r
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\n" ); document.write( "\n" ); document.write( "Clearly, if

, then

, and we have one possible answer.\r
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\n" ); document.write( "\n" ); document.write( "We know that

because

is not evenly divisible by 5.\r
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\n" ); document.write( "\n" ); document.write( "Note that for

to have an integer solution,

where

. But our previous work bounds the possible values for

between 1 and 14, so the only two possible values are 7 and 14.\r
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\n" ); document.write( "\n" ); document.write( "Hence, 12 lbs salmon and 7 lbs trout, or 2 lbs salmon and 14 lbs trout.
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\n" ); document.write( "John
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\n" ); document.write( "My calculator said it, I believe it, that settles it
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